Locating the CEPs of QCD phase transitions via the dyson-schwinger equation approach of QCD

We describe concisely the Dyson-Schwinger (DS) equation approach of QCD and review briefly the progress of the study on the QCD phase transitions with reporting some new results and fo-cussing on the existence and location of the CEP, via the Dyson-Schwinger equation approach of QCD. By calculating and analyzing the chiral susceptibility, the quark number density fluctuations, and some of the thermal properties in the sophisticated continuum QCD approach, we show that there exist a CEP for the chiral phase transition, and so does for the confinement–deconfinement phase transition. The CEP for the chiral phase transition locates at (T_E , µ_E,B)^∼= (0.90 , 2.33)T_c ^χ with T_c ^χ = 143 MeV, and that for the confinement–deconfinement phase transition is approximately at (T_E , µ_E,B)^∼= (0.85 , 2.50)T_c ^χ . We also show that the existence and the location of the CEPs in theoretical investigations are governed by the (confinement) interaction length scale embodied in the approach and the reason for the fact that different kind approaches give quite distinct locations for the CEP just results from that difference.